In a bowl, combine the flour, baking soda, cinnamon, nutmeg, all spice and salt.
In another large bowl, combine brown sugar and oil with a handheld or stand mixer fitted with a paddle attachment on medium speed. Beat in the yogurt for about a minute until fully combined. Add one egg one at a time, beating well after each addition. Mix in the vanilla and set aside.
With a spatula, manually stir and fold in the dry ingredients into the wet ingredients until just combined. Do not over mix.
Gently fold in the finely shredded carrots and toasted nuts.
Pour the batter into prepared springform pan.
Bake cake for 34-40 minutes or until toothpick inserted in the center comes out clean.